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Simplifying 20q2 + -41qr + 20r2 = 0 Reorder the terms: -41qr + 20q2 + 20r2 = 0 Solving -41qr + 20q2 + 20r2 = 0 Solving for variable 'q'. Factor a trinomial. (4q + -5r)(5q + -4r) = 0Subproblem 1
Set the factor '(4q + -5r)' equal to zero and attempt to solve: Simplifying 4q + -5r = 0 Solving 4q + -5r = 0 Move all terms containing q to the left, all other terms to the right. Add '5r' to each side of the equation. 4q + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 4q + 0 = 0 + 5r 4q = 0 + 5r Remove the zero: 4q = 5r Divide each side by '4'. q = 1.25r Simplifying q = 1.25rSubproblem 2
Set the factor '(5q + -4r)' equal to zero and attempt to solve: Simplifying 5q + -4r = 0 Solving 5q + -4r = 0 Move all terms containing q to the left, all other terms to the right. Add '4r' to each side of the equation. 5q + -4r + 4r = 0 + 4r Combine like terms: -4r + 4r = 0 5q + 0 = 0 + 4r 5q = 0 + 4r Remove the zero: 5q = 4r Divide each side by '5'. q = 0.8r Simplifying q = 0.8rSolution
q = {1.25r, 0.8r}
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